file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.comp_inv_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nf : Z ⟶ Y\ng : Z ⟶ X\nH : f ≫ α.inv = g\n⊢ f = g ≫ α.hom",
"tactic": "simp [H.symm]"
},
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nf : ... | [
230,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.right_inv | [
{
"state_after": "case refine_1\nR : Type u_2\nA : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nx : A[X]\n⊢ ∀ (p q : A[X]),\n ↑(toFunAlgHom R A) (invFun R A p) = p →\n ↑(toFunAlgHom R A) (invFun R A q) = q → ↑(toFunAlgHom R A) (invFun R A (p + q)) = p + q\n\ncase refine_2... | [
178,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.ext | [] | [
109,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.Tendsto.prod_map | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ✝ : Type ?u.29553\nι : Sort ?u.29556\ns : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\nδ : Type u_1\nf : α → γ\ng : β → δ\na : Filter α\nb : Filter β\nc : Filter γ\nd : Filter δ\nhf : Tendsto f a c\nhg : Tendsto g b d\n⊢ map f a ×ˢ map g b ≤ c ×ˢ d... | [
371,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_congr_nhds | [] | [
503,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.dvd_sum | [
{
"state_after": "ι : Type ?u.115200\nα : Type u_1\nβ : Type ?u.115206\nγ : Type ?u.115209\ninst✝ : Semiring α\na : α\ns✝ : Multiset α\nx : α\ns : Multiset α\nih : (∀ (x : α), x ∈ s → a ∣ x) → a ∣ sum s\nh : ∀ (x_1 : α), x_1 ∈ x ::ₘ s → a ∣ x_1\n⊢ a ∣ x + sum s",
"state_before": "ι : Type ?u.115200\nα : Typ... | [
355,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.addNat_subNat | [] | [
1597,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Basis.det_isEmpty | [
{
"state_after": "case H\nR : Type u_2\ninst✝⁷ : CommRing R\nM : Type u_3\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nM' : Type ?u.2538346\ninst✝⁴ : AddCommGroup M'\ninst✝³ : Module R M'\nι : Type u_1\ninst✝² : DecidableEq ι\ninst✝¹ : Fintype ι\ne : Basis ι R M\ninst✝ : IsEmpty ι\nv : ι → M\n⊢ ↑(det e) v = ↑... | [
544,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.ext | [] | [
262,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_iInf_of_ul_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι✝ : Sort x\nκ : ι✝ → Sort ?u.42456\na a₁ a₂ : α\nb b₁ b₂ : β\nl : α → β\nu : β → α\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\ngi : GaloisInsertion l u\nι : Sort x\nf : ι → α\nhf : ∀ (i : ι), u (l (f i)) = f i\n⊢ ... | [
583,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_zero_eq_preimage_ball | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1017930\nR' : Type ?u.1017933\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1017939\n𝕜₃ : Type ?u.1017942\n𝕝 : Type ?u.1017945\nE : Type u_1\nE₂ : Type ?u.1017951\nE₃ : Type ?u.1017954\nF : Type ?u.1017957\nG : Type ?u.1017960\nι : Type ?u.1017963\ninst✝⁶ : Semino... | [
819,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.le_card_sdiff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.40449\ns✝ t✝ : Finset α\nf : α → β\nn : ℕ\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ card (t \\ (s ∩ t)) ≤ card (t \\ s)",
"tactic": "rw [sdiff_inter_self_right t s]"
}
] | [
445,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | finiteDimensional_of_isCompact_closed_ball₀ | [
{
"state_after": "𝕜 : Type u\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁵ : AddCommGroup F'\ninst✝⁴ : Module 𝕜 F'\ninst✝³ : TopologicalSpace F'\ninst✝² : To... | [
478,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.card_nthRoots | [
{
"state_after": "case inl\nM : Type ?u.3547388\nN : Type ?u.3547391\nG : Type ?u.3547394\nR : Type u_1\nS : Type ?u.3547400\nF : Type ?u.3547403\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh✝ : IsPrimitiveRoot ζ✝ k\ninst✝ : IsDomain R\nζ ... | [
835,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
8
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.comapDomain_smul | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type u_1\ninst✝² : Monoid γ\ninst✝¹ : (i : ι) → AddMonoid (β i)\ninst✝ : (i : ι) → DistribMulAction γ (β i)\nh : κ → ι\nhh : Function.Injective h\nr : γ\nf : Π₀ (i : ι), β i\ni✝ : κ\n⊢ ... | [
1340,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.exp_eq | [
{
"state_after": "q : ℍ\n⊢ Commute (↑q.re) (im q)",
"state_before": "q : ℍ\n⊢ exp ℝ q = exp ℝ q.re • (↑(Real.cos ‖im q‖) + (Real.sin ‖im q‖ / ‖im q‖) • im q)",
"tactic": "rw [← exp_of_re_eq_zero q.im q.im_re, ← coe_mul_eq_smul, ← exp_coe, ← exp_add_of_commute,\n re_add_im]"
},
{
"state_after": ... | [
109,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.finOrthonormalBasis_orientation | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nn : ℕ\nhn : 0 < n\nh : finrank ℝ E = n\nx : Orientation ℝ E (Fin n)\nthis : Nonempty (Fin n)\n⊢ Basis.orientation (OrthonormalBasis.toBasis (Orientation.finOrthonormalBasis hn h x)) = x",
"state_before": "E : Type ... | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_biInf | [
{
"state_after": "α : Type u_3\nβ : Type ?u.1581955\nγ : Type ?u.1581958\nγ₂ : Type ?u.1581961\nδ : Type u_2\nι✝ : Sort y\ns✝ t u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : BorelSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\ninst✝⁷ : BorelSpace β\ninst✝⁶ : T... | [
1305,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.subset_closure | [] | [
702,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | ball_mono | [] | [
635,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Data/Set/Image.lean | Set.forall_subset_range_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.76965\nι : Sort ?u.76968\nι' : Sort ?u.76971\nf✝ : ι → α\ns t : Set α\nf : α → β\np : Set β → Prop\n⊢ (∀ (s : Set β), s ⊆ range f → p s) ↔ ∀ (a : Set β), a ∈ 𝒫 range f → p a",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.76965\nι : Sort ... | [
818,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_mod | [
{
"state_after": "no goals",
"state_before": "a b n : Nat\n⊢ a * b % n = a % n * (b % n) % n",
"tactic": "conv => lhs; rw [\n ← mod_add_div a n, ← mod_add_div b n, Nat.add_mul, Nat.mul_add, Nat.mul_add,\n Nat.mul_assoc, Nat.mul_assoc, ← Nat.mul_add n, add_mul_mod_self_left,\n Nat.mul_comm _ (n * (b /... | [
782,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
778,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_mul_left_right | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd n (m * n) = n",
"tactic": "rw [gcd_comm, gcd_mul_left_left]"
}
] | [
153,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
152,
9
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_monoidHom_mk | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.monotone_filter_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.208071\nγ : Type ?u.208074\np✝ : α → Prop\ninst✝² : DecidablePred p✝\ns : Multiset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∀ (b : α), p b → q b\nl : List α\n⊢ ∀ (a : α), decide (p a) = true → decide (q ... | [
1962,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1959,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_le_one_of_le_one | [] | [
231,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.dvd_gcd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns : Multiset α\na : α\n⊢ a ∣ gcd 0 ↔ ∀ (b : α), b ∈ 0 → a ∣ b",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommM... | [
158,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.const_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝² : AddMonoid α\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Periodic f c\na : γ\nx : α\n⊢ (fun x => f (a • x)) (x + a⁻¹ • c) = (fun x => f (a • x)) x",
"tactic": "simpa only... | [
113,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
11
] |
Mathlib/Data/Set/Image.lean | Set.range_inclusion | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type ?u.97081\nγ : Type ?u.97084\nι : Sort ?u.97087\nι' : Sort ?u.97090\nf : ι → α\ns t : Set α\nh : s ⊆ t\nx : α\nhx : x ∈ t\n⊢ { val := x, property := hx } ∈ range (inclusion h) ↔ { val := x, property := hx } ∈ {x | ↑x ∈ s}",
"state_before": "α : Type u_1\nβ ... | [
1139,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | Differentiable.clm_comp | [] | [
98,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_mul_ideal | [] | [
292,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.den_coe | [] | [
469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Std/Data/Option/Basic.lean | Option.some_inj | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b : α\n⊢ some a = some b ↔ a = b",
"tactic": "simp"
}
] | [
24,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.pure_apply | [] | [
48,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/NumberTheory/Liouville/Measure.lean | volume_iUnion_setOf_liouvilleWith | [
{
"state_after": "⊢ ↑↑volume {x | ∃ i, 2 < i ∧ LiouvilleWith i x} = 0",
"state_before": "⊢ ↑↑volume (⋃ (p : ℝ) (_ : 2 < p), {x | LiouvilleWith p x}) = 0",
"tactic": "simp only [← setOf_exists, exists_prop]"
},
{
"state_after": "⊢ ↑↑volume\n (⋃ (m : ℤ),\n (fun x => x + ↑m) ⁻¹'\n ... | [
111,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.coe_copy | [] | [
1070,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.count_le | [] | [
505,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Order/Compare.lean | LT.lt.cmp_eq_lt | [] | [
271,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.union_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.170514\nγ : Type ?u.170517\ninst✝ : DecidableEq α\ns t u : Multiset α\na b : α\n⊢ s ∪ 0 = s",
"tactic": "simp [union_def]"
}
] | [
1737,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
9
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_aleph0 | [] | [
1616,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1615,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.moveRight_mk_right | [
{
"state_after": "no goals",
"state_before": "xr : Type u_1\ni : xr\nxl : Type u_1\nxL : xl → PGame\nxR : xr → PGame\nj : RightMoves (xR i)\n⊢ Subsequent (PGame.moveRight (xR i) j) (mk xl xr xL xR)",
"tactic": "pgame_wf_tac"
}
] | [
313,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
9
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_canonicalEquiv_apply | [
{
"state_after": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.803106\ninst✝¹ : CommRing P''\ninst✝ : Algebra R P''\nloc... | [
913,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow₀ | [
{
"state_after": "case refl\nβ : Type ?u.287678\nA : Type ?u.287681\nG : Type ?u.287684\nM : Type u_1\nR : Type ?u.287690\ninst✝ : LinearOrderedCommGroupWithZero M\na : M\nm n : ℕ\nha : 1 < a\n⊢ a ^ m < a ^ Nat.succ m\n\ncase step\nβ : Type ?u.287678\nA : Type ?u.287681\nG : Type ?u.287684\nM : Type u_1\nR : Ty... | [
791,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.bijective | [] | [
228,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
11
] |
Std/Data/Option/Lemmas.lean | Option.some_get | [] | [
33,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
32,
9
] |
Std/Data/Option/Lemmas.lean | Option.ne_none_iff_isSome | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\no : Option α✝\n⊢ o ≠ none ↔ isSome o = true",
"tactic": "cases o <;> simp"
}
] | [
73,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
73,
1
] |
Mathlib/Topology/CompactOpen.lean | QuotientMap.continuous_lift_prod_right | [
{
"state_after": "X₀ : Type u_1\nX : Type u_2\nY : Type u_3\nZ : Type u_4\ninst✝⁴ : TopologicalSpace X₀\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : LocallyCompactSpace Y\nf : X₀ → X\nhf : QuotientMap f\ng : Y × X → Z\nhg : Continuous fun p => g (p.fst, f p.snd... | [
497,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/Int/SuccPred.lean | Nat.cast_int_covby_iff | [
{
"state_after": "a b : ℕ\n⊢ ↑a + 1 = ↑b ↔ a + 1 = b",
"state_before": "a b : ℕ\n⊢ ↑a ⋖ ↑b ↔ a ⋖ b",
"tactic": "rw [Nat.covby_iff_succ_eq, Int.covby_iff_succ_eq]"
},
{
"state_after": "no goals",
"state_before": "a b : ℕ\n⊢ ↑a + 1 = ↑b ↔ a + 1 = b",
"tactic": "exact Int.coe_nat_inj'"
}
... | [
97,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.eq_two_or_odd' | [] | [
501,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ico.coe_ne_zero | [] | [
208,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_lt_iff_mul_self_lt | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a < abs b ↔ abs a * abs a < abs b * abs b",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a < abs b ↔ a * a < b * b",
"tactic": "rw [← abs_mul_abs_self, ← abs_mul_abs_self b]"
},
{
"state... | [
93,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_coe_nat | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁵ : CommSemiring R\nA : Type u_2\ninst✝⁴ : CommSemiring A\ninst✝³ : Algebra R A\nM : Type u_1\ninst✝² : AddCommMonoid M\ninst✝¹ : Module A M\ninst✝ : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : ℕ\n⊢ ↑D ↑n = 0",
"tactic": "r... | [
155,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotone_app | [] | [
328,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_le_one | [] | [
1271,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_subset_sInter | [] | [
1075,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_singleton_iff | [] | [
1491,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1490,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_sup | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.107383\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nH₁ H₂ : Subgraph G\n⊢ ∀ (x y : V),\n Quotient.mk (Sym2.Rel.setoid V) (x, y) ∈ edgeSet (H₁ ⊔ H₂) ↔\n Quotient.mk (Sym2.Rel.setoid V) (x, y) ∈ edgeSet H₁ ∪ edgeSet ... | [
554,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.eq | [] | [
693,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eventually_nhdsWithin | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.34147\nδ : Type ?u.34150\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne✝ : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ne : LocalHomeomorph α β\nx : α\np : β → Prop\ns : Set α\nhx :... | [
411,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.smul_eq_C_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na✝ b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\na : R\n⊢ a • p = ↑C a * p",
"tactic": "simp [ext_iff]"
}
] | [
362,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_smul_const | [
{
"state_after": "case pos\nα : Type u_3\nβ : Type ?u.4211708\nE : Type u_2\nF : Type ?u.4211714\ninst✝¹¹ : MeasurableSpace α\nι : Type ?u.4211720\ninst✝¹⁰ : NormedAddCommGroup E\nμ : MeasureTheory.Measure α\n𝕜✝ : Type ?u.4326528\ninst✝⁹ : IsROrC 𝕜✝\ninst✝⁸ : NormedSpace 𝕜✝ E\ninst✝⁷ : NormedAddCommGroup F\n... | [
1214,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1206,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_union₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.296515\nγ : Type ?u.296518\nδ : Type ?u.296521\nι : Type ?u.296524\nR : Type ?u.296527\nR' : Type ?u.296530\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
1724,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1722,
1
] |
Mathlib/Topology/Separation.lean | IsCompact.binary_compact_cover | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nα : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nγ : Type ?u.133233\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space α\nK U V : Set α\nhK : IsCompact K\nhU : IsOpen U\nhV : IsOpen V\nh2K : K ⊆ U ∪ V\nO₁ O₂ : Set α\nh1O₁ : ... | [
1327,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1319,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.invOf_mul_self | [] | [
72,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | TopologicalSpace.IsTopologicalBasis.borel_eq_generateFrom | [] | [
101,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.padicValRat_le_padicValRat_iff | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nn₁ n₂ d₁ d₂ : ℤ\nhn₁ : n₁ ≠ 0\nhn₂ : n₂ ≠ 0\nhd₁ : d₁ ≠ 0\nhd₂ : d₂ ≠ 0\nhf1 : multiplicity.Finite (↑p) (n₁ * d₂)\n⊢ padicValRat p (n₁ /. d₁) ≤ padicValRat p (n₂ /. d₂) ↔ ∀ (n : ℕ), ↑p ^ n ∣ n₁ * d₂ → ↑p ^ n ∣ n₂ * d₁",
"state_before": "p : ℕ\nhp : Fact (Nat... | [
338,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.mul_inv' | [] | [
207,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.theory_model_iff | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\nN : Type u_4\nP : Type ?u.262800\nQ : Type ?u.262803\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\ninst✝ : Structure L Q\nf : M ↪ₑ[L] N\nT : Theory L\n⊢ M ⊨ T ↔ N ⊨ T",
"tactic": "simp only [Theory.model... | [
118,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.natPred_injective | [] | [
57,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPushforward_top | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF✝ : C ⥤ D\nX✝ Y Z : C\nf : Y ⟶ X✝\nS R : Sieve X✝\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nF : C ⥤ D\nX : C\n⊢ generate (functorPushforward F ⊤).arrows = ⊤",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type... | [
713,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_lt_log | [
{
"state_after": "x y : ℝ\nhx : 0 < x\nh : x < y\n⊢ log x < log y",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ x < y → log x < log y",
"tactic": "intro h"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 < x\nh : x < y\n⊢ log x < log y",
"tactic": "rwa [← exp_lt_exp, exp_log... | [
151,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/List/Sigma.lean | List.nil_kunion | [] | [
686,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_subset_iff_exists_mem_not_mem | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α✝\ns✝ s₁ s₂ t✝ t₁ t₂ u : Set α✝\nα : Type u_1\ns t : Set α\n⊢ ¬s ⊆ t ↔ ∃ x, x ∈ s ∧ ¬x ∈ t",
"tactic": "simp [subset_def]"
}
] | [
715,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasInitial C\n⊢ zeroIsoInitial.hom = 0",
"tactic": "ext"
}
] | [
320,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_iff_not_even | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Odd n ↔ ¬Even n",
"tactic": "rw [not_even_iff, odd_iff]"
}
] | [
60,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Order/BoundedOrder.lean | Antitone.forall | [] | [
584,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.copy_eq | [] | [
134,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/PFun.lean | PFun.dom_mk | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Fintype.prod_empty | [] | [
2011,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2009,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | MonoidHom.coe_dfinsupp_prod | [] | [
2256,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2254,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_eventually_measure_zero_of_singular | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.1306254\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
208,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multiequalizer.ιPi_π | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nI : MulticospanIndex C\ninst✝² : HasMultiequalizer I\ninst✝¹ : HasProduct I.left\ninst✝ : HasProduct I.right\na : I.L\n⊢ equalizer.ι (MulticospanIndex.fstPiMap I) (MulticospanIndex.sndPiMap I) ≫ Pi.π I.left a =\n (limit.isoLimitCone\n {\n ... | [
831,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Logic/Nonempty.lean | Nonempty.map2 | [] | [
147,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
11
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_eq_self_iff | [
{
"state_after": "case mp\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\np : P\n⊢ ↑(↑(orthogonalProjection ... | [
387,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | MonoidHomClass.bound_of_antilipschitz | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type u_1\n𝕜 : Type ?u.408704\nα : Type ?u.408707\nι : Type ?u.408710\nκ : Type ?u.408713\nE : Type u_2\nF : Type u_3\nG : Type ?u.408722\ninst✝³ : SeminormedGroup E\ninst✝² : SeminormedGroup F\ninst✝¹ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E\nr ... | [
1017,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.integrable_of_boundedContinuous_to_nnreal | [
{
"state_after": "Ω : Type u_1\ninst✝³ : MeasurableSpace Ω\ninst✝² : TopologicalSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nf : Ω →ᵇ ℝ≥0\n⊢ HasFiniteIntegral (NNReal.toReal ∘ ↑f)",
"state_before": "Ω : Type u_1\ninst✝³ : MeasurableSpace Ω\ninst✝² : TopologicalSpace Ω\... | [
669,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.liftAddHom_symm_apply_apply | [] | [
453,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.card_quotient_normalizer_modEq_card_quotient | [
{
"state_after": "G : Type u\nα : Type v\nβ : Type w\ninst✝¹ : Group G\ninst✝ : Fintype G\np n : ℕ\nhp : Fact (Nat.Prime p)\nH : Subgroup G\nhH : Fintype.card { x // x ∈ H } = p ^ n\n⊢ Fintype.card ↑(MulAction.fixedPoints { x // x ∈ H } (G ⧸ H)) ≡ Fintype.card (G ⧸ H) [MOD p]",
"state_before": "G : Type u\n... | [
552,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.coe_comp | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isConnected_Ici | [] | [
466,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_coe_nat_div_add_atTop | [
{
"state_after": "case refine'_1\nα : Type ?u.10393\nβ : Type ?u.10396\nι : Type ?u.10399\n𝕜 : Type u_1\ninst✝⁵ : DivisionRing 𝕜\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : Algebra ℝ 𝕜\ninst✝¹ : ContinuousSMul ℝ 𝕜\ninst✝ : TopologicalDivisionRing 𝕜\nx : 𝕜\n⊢ ℕ → 𝕜\n\ncase refine'_2\nα :... | [
80,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.tan_int_mul_pi_div_two | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ ∃ k, ↑n * π / 2 = ↑k * π / 2",
"tactic": "use n"
}
] | [
60,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.has_limits_of_equivalence | [] | [
273,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bodd_bit | [
{
"state_after": "b : Bool\nn : ℤ\n⊢ bodd (2 * n + bif b then 1 else 0) = b",
"state_before": "b : Bool\nn : ℤ\n⊢ bodd (bit b n) = b",
"tactic": "rw [bit_val]"
},
{
"state_after": "no goals",
"state_before": "b : Bool\nn : ℤ\n⊢ bodd (2 * n + bif b then 1 else 0) = b",
"tactic": "cases b ... | [
169,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.coe_id | [] | [
433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_top | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝³ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝² : CommRing S\ninst✝¹ : Algebra R S\nP : Type ?u.30644\ninst✝ : CommRing P\n⊢ coeSubmodule S ⊤ = 1",
"tactic": "rw [coeSubmodule, Submodule.map_top, Submodule.one_eq_range]"
}
] | [
58,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.nnabs_coe | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\n⊢ ↑nnabs ↑x = x",
"tactic": "simp"
}
] | [
1071,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Mathlib/Order/Directed.lean | isBot_or_exists_lt | [] | [
287,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | convexOn_rpow | [
{
"state_after": "case inl\nhp : 1 ≤ 1\n⊢ ConvexOn ℝ (Ici 0) fun x => x ^ 1\n\ncase inr\np : ℝ\nhp✝ : 1 ≤ p\nhp : 1 < p\n⊢ ConvexOn ℝ (Ici 0) fun x => x ^ p",
"state_before": "p : ℝ\nhp : 1 ≤ p\n⊢ ConvexOn ℝ (Ici 0) fun x => x ^ p",
"tactic": "rcases eq_or_lt_of_le hp with (rfl | hp)"
},
{
"stat... | [
282,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.compContinuousLinearMap_apply | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.